Third post-Newtonian constrained canonical dynamics for binary point masses in harmonic coordinates

1550-7998=20 The conservative dynamics of two point masses given in harmonic coordinates up to the third postNewtonian order is treated within the framework of constrained canonical dynamics. A representation of the approximate Poincaré algebra is constructed with the aid of Dirac brackets. Uniqueness of the generators of the Poincaré group or the integrals of motion is achieved by imposing their action on the point mass coordinates to be identical with that of the usual infinitesimal Poincaré transformations. The second post-Coulombian approximation to the dynamics of two point charges as predicted by Feynman-Wheeler electrodynamics in Lorentz gauge is treated similarly.